Abstract Inspired by geometric mean metric learning(GMML), a convex discriminant canonical correlation analysis(CDCA) is proposed. The learning of two projection matrices is transformed into a geodesic convex problem of metric learning. Thereby a closed form solution is acquired and simultaneously discriminant fused features are extracted directly. The experiments on artificial and real datasets verify the effectiveness of CDCA.
About author:: (JIANG Fan, born in 1985, master student. His research interests include pattern recognition and machine learning.) (CHEN Songcan(Corresponding author), born in 1962, Ph.D., professor. His research interests include pattern recognition and machine learning.)
[1] HARDOON D R, SZEDMAK S, SHAWE-TAYLOR J. Canonical Correlation Analysis: An Overview with Application to Learning Methods. Neural Computation, 2004, 16(12): 2639-2664. [2] HOTELLING H. Relations between Two Sets of Variates. Biometrika, 1936, 28(3/4): 321-377. [3] XU C, TAO D C, XU C. A Survey on Multi-view Learning[J/OL]. [2017-03-21]. https://arxiv.org/pdf/1304.5634.pdf. [4] ROSS A, JAIN A K. Multimodal Biometrics: An Overview // Proc of the 12th European Signal Processing Conference. Washington, USA: IEEE, 2004: 1221-1224. [5] SUN Q S, ZENG S G, LIU Y, et al. A New Method of Feature Fusion and Its Application in Image Recognition. Pattern Recognition, 2005, 38(12): 2437-2448. [6] SUN T K, CHEN S C, YANG J Y, et al. A Supervised Combined Feature Extraction Method for Recognition // Proc of the IEEE International Conference on Data Mining. Washington, USA: IEEE, 2008: 1043-1048. [7] SUN T K, CHEN S C, YANG J Y, et al. A Novel Method of Combined Feature Extraction for Recognition // Proc of the 8th IEEE International Conference on Data Mining. Washington, USA: IEEE, 2008: 1043-1048. [8] PENG Y, ZHANG D Q, ZHANG J C. A New Canonical Correlation Analysis Algorithm with Local Discrimination. Neural Processing Letters, 2010, 31(1). DOI: 10.1007/s11063-009-9123-3. [9] SU S Z, GE H W, YUAN Y H. Multi-patch Embedding Canonical Correlation Analysis for Multi-view Feature Learning. Journal of Vi-sual Communication and Image Representation, 2016, 41: 47-57. [10] JI H K, SUN Q S, YUAN Y H, et al. Fractional-Order Embe-dding Supervised Canonical Correlations Analysis with Applications to Feature Extraction and Recognition. Neural Processing Letters, 2017, 45(1): 279-297. [11] SUN Q S, LIU Z D, HENG P A, et al. A Theorem on the Gene-ralized Canonical Projective Vectors. Pattern Recognition, 2005, 38(3): 449-452. [12] 周旭东,陈晓红,陈松灿.增强组合特征判别性的典型相关分析.模式识别与人工智能, 2012, 25(2): 285-291. (ZHOU X D, CHEN X H, CHEN S C. Combined-Feature-Discriminability Enhanced Canonical Correlation Analysis. Pattern Recognition and Artificial Intelligence, 2012, 25(2): 285-291.) [13] FISHER R A. The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics, 1936, 7(2): 179-188. [14] ZHAO F, QIAO L S, SHI F, et al. Feature Fusion via Hierarchical Supervised Local CCA for Diagnosis of Autism Spectrum Disorder. Brain Imaging and Behavior, 2016. DOI: 10.1007/s11682-016-9587-5. [15] HAGHIGHAT M, ABDEL-MOTTALEB M, ALHALABI W S. Discriminant Correlation Analysis for Feature Level Fusion with Application to Multimodal Biometrics // Proc of the 41st IEEE Interna- tional Conference on Acoustics, Speech and Signal Processing. Washington, USA: IEEE, 2016: 1866-1870. [16] ZADEH P H, HOSSEINI R, SRA S. Geometric Mean Metric Learning // Proc of the 33rd International Conference on Machine Learning. New York, USA: ACM, 2016: 2464-2471. [17] HOEGAERTS L, SUYKENS J A K, VANDEWALLE J, et al. Subset Based Least Squares Subspace Regression in RKHS. Neurocomputing, 2005, 63: 293-323. [18] BHATIA R. Positive Definite Matrices. Princeton, USA: Princeton University Press, 2009. [19] ARSIGNY V, FILLARD P, PENNEC X, et al. Geometric Means in a Novel Vector Space Structure on Symmetric Positive-Definite Matrices. SIAM Journal on Matrix Analysis and Applications, 2007, 29(1): 328-347. [20] VAN BREUKELEN M, DUIN R P W, TAX D M J, et al. Handwritten Digit Recognition by Combined Classifiers. Kybernetika, 1998, 34(4): 381-386. [21] LAMPERT C H, NICKISCH H, HARMELING S. Learning to Detect Unseen Object Classes by Between-Class Attribute Transfer // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2009: 951-958. [22] HAO X K, YAO X H, YAN J W, et al. Identifying Multimodal Intermediate Phenotypes between Genetic Risk Factors and Disease Status in Alzheimer's Disease. Neuroinformatics, 2016, 14(4): 439-452. [23] HUANG G B, ZHU Q Y, SIEW C K. Extreme Learning Machine: Theory and Applications. Neurocomputing, 2006, 70(1/2/3): 489-501. [24] SAKAR C O, KURSUN O. Discriminative Feature Extraction by a Neural Implementation of Canonical Correlation Analysis. IEEE Transactions on Neural Networks and Learning Systems, 2017, 28(1): 164-176.
2017, Vol. 30 
